Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #1951 |
196 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=f,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^42,d^b=dg872 conjugacy classes — view the full character table.
| maximal subgroup of | #25013280, #25013283, #25013308, … |
| maximal normal subgroup of | #25013280, #25013283, #25013308, … |
| maximal quotient of | #24995208, #24995218, #24995228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 5290);